While significant progress has been made on key cosmological questions, many remain unanswered: What happened during the first moments of the big bang? What is dark energy? What were the properties of the first stars?
Classically, arithmetic is the study of rational or integral solutions of diophantine equations and geometry the study of lines and conics. From the modern standpoint, these areas are synthesized in the study of rational and integral points on algebraic varieties over nonclosed fields. A major insight of the 20th century was that the arithmetic properties...
A talk on recent advances in methods and instrumentation that combine genetically encoded molecular sensors, optical imaging and virtual-reality systems to measure neural-circuit dynamics in the mouse brain during virtual navigation and decision making.
Most sensory stimuli in the natural world exhibit strong statistical regularities. A proposed general principle of sensory neuroscience is that the brain’s circuitry is designed to take advantage of these statistical regularities.
In recent years, homological knot invariants have been gaining momentum in both mathematics and physics, and recent developments promise it will only be growing. Therefore, a symposium on “the physics of knot homologies” is very timely. Moreover, this subject is intimately connected with another active area of research at the interface of geometry and physics:...
The mind and brain can be thought of as computational systems — but what kinds of computations do they carry out, and what kinds of mathematics can best characterize these computations? Josh Tenenbaum attempts to answer these questions through the integration of disparate branches of mathematics and paradigms of computation.
The talk describes (dis)similarity distances between pairs of two-dimensional surfaces (embedded in three-dimensional space) that use both local structures and global information in the surfaces.
Organizers: Sanjeev Arora, Uriel Feige, Michel Goemans & David Shmoys Many of the striking advances in theoretical computer science over the past two decades concern approximation algorithms, which compute provably near-optimal solutions to NP-hard optimization problems. Yet the approximability of several fundamental problems such as TSP, Graph Coloring, Graph Partitioning etc. remains an open question. For...
Resting-state functional magnetic resonance imaging (fMRI) has been used to identify consistent functional patterns in neurotypical individuals, as well as changes in neurologic and psychiatric diseases.
Resting-state functional magnetic resonance imaging (fMRI) has been used to identify consistent functional patterns in neurotypical individuals, as well as changes in neurologic and psychiatric diseases.
February 3-9, 2013 The goal of our meeting will be to explore exotic quantum states of matter, with a particular focus on the role of quantum entanglement. A variety of new tools arising from both the study of quantum field theoretic techniques in condensed matter physics, and from the "holographic" duality between field theories and...
Probability theory was devised in order to understand gambling, but now is the underpinning of statistics, without which we would be clueless in our complex society. Yet probability itself is a mysterious quantity, hard to define, and awkward for our human intuition to cope with. Does it even exist, except in our minds?
